How to know when to stop and a problem is done

[Newtons Apple]

Hey everyone, so I was working on problem that resulted in this:

y=√4-x^2 ( the 4-x^2 is under the square root)

and I was stumped as to what to do next... then later finally giving up, I realized that that was the end of the problem, and that it would just end in either negative or positive. This isn't the first time something like this has happened. How do you know when you're done working on a problem? Often times, I'd think I was done with a problem, and I had simplified is as low as possible, but then whamo! I was supposed to factor it, or do something else to it... How do you know if you've reached the end, or if there is more to do?

 

[HallsofIvy]

Well, you haven't said what the problem is! That's the crucial point. Every problem asks you to do some specific thing or answer a specific question. You are done when you have done what you were asked to do or answered the question.

 

[Newtons Apple]

lol, ok, well the problem was:
Determine whether the equation represents y as a function of x

x^2 + y^2 = 4

I moved the x^2 over to get y by itself etc.. and I square rooted y^2 to rip off the square. I was looking at the square root over the reamaing 4-x^2 and puzzled, not realizing that it was the end! Like I said, its not just this time, I always do that or never realizing if there's more steps involved, or if the equation or expression can be worked on more...

 

[jsndacruz]

In that case you need to think about what it means for 'y to be a function of x.' In the simplest of terms, it is when you can write 'y' on one side of the equation, and all constants and 'x' terms on the other.

Do you have another example of when you found yourself in an endless loop? Or is it for similar types of problems?